"IT'S RADIOHEAD NIGHT!" shouts the menu poster outside the bar'n'grill just inside the O2 Arena's doors. "PARTY LIKE A ROCK STAR!" At first you just roll your eyes at the crater-sized disconnect between knee-jerk corporate food marketing and the ethos of the band whose name is being taken in vain in block caps. Even when Radiohead were a conventional outfit, singing grunge-pop ditties such as Creep, their image was that of haughty refuseniks, not shirtless Lotharios lairily gnawing buffalo wings. Thom Yorke had publicly aligned his band with the aesthetically disaffected, the creeps and the weirdos.

Twenty years on, Radiohead remain one of the biggest bands in the world, one uncommonly in control of their own destiny. They are label-less and immune to corporate pressure. The last laugh is very much theirs. So your eye-roll becomes more of a subtle air-punch. There is no little heroism in the fact that the Oxfordshire five-piece can come to giant sheds like these and sell them out with their jazz-tinged electronic rock, sung in falsetto by a nervy mendicant type sporting a beard and a top-knot.

Thom Yorke – just a day past his 44th birthday – is an especially magnetic presence tonight, dancing like a marionette plugged into the mains, his good mood evident. He has to break off from the start of Daily Mail, he's chuckling so much. "A quality newspaper," he mugs.

The slightly nerdy impression of Radiohead's first London gig in four years is that tricksy, headphone-friendly albums such as last year's The King of Limbs can, when placed in an arena, sound quite like proper arena rock. Radiohead's songs can be simple, of course. Karma Police, from 1997's OK Computer, gets an airing and a huge cheer. By contrast, Like Spinning Plates, previously a staticky wobble on record, becomes an affecting piano ballad. Separator, too, has easy-going breakbeats, country guitar and a consolatory air that is rare in Radiohead's emotional palette. It's not all cerebral stuff.

But mostly, Radiohead are here to unleash fiercely discomfiting rhythmic workouts that, tonight, require two real drummers (Phil Selway and touring helpmeet Clive Deamer, of Portishead) and quite often some programming too. On an emotional There There in the encore, it's four drummers: guitarists Jonny Greenwood and Ed O'Brien get to bash mini-kits.

It all sounds utterly live. A tricksy Lotus Flower is the opener, and it virtually roars with real-time musicianship, not mere harnessed technology. Fringe flapping, Jonny Greenwood dashes around all night, playing a sequence of alternative instruments – tambourine, keyboard, laptop, some kind of Theremin and effects pedals.

The visual technology is impressive. An arrangement of 10 screens hang in the air, tilting at a different angle for every song. Radiohead frequently make the most of the dead air space between their heads and the ceiling; their 2008 tour featured some terrific light-up stalactites. This year's hanging screens display live feeds of the various band members playing intently (they are probably counting hard in their heads). At one splendid point, on 15 Step, the screens unite and point downwards to form a bright turquoise light-roof over the band. It's like one of those lights that helps seasonal affective disorder, but on an industrial scale.

The King of Limbs was not quite the big-selling, high-charting two fingers to corporate convention that its predecessor, In Rainbows, was. It was the first of their albums to fail to claim the Number 1 chart spot in the UK since 1995's The Bends. And this tour is pushing it a year late, and relatively gently in this country: this is one of only three UK gigs. By contrast, their summer tour of the US was more comprehensive. But the prevailing mood in the crowd is one of rapt attention, repaid by a double encore.

Post- Limbs, Radiohead's direction of travel seems to be signposted by the slinky new track Identikit, which features the dual vocals of Yorke and O'Brien. It's by far their most accessible tune for some time. Whether or not it signposts anything of significance is, of course, unclear. What's plain tonight, though, is that this is a band taking their rock responsibilities seriously. Having picked up an entire demographic and, with 2000's Kid A, plonked them down somewhere very much left of field, Radiohead can still do arenas very nicely indeed.